Spanning Distribution Trees of Graphs


IEICE TRANSACTIONS on Information and Systems   Vol.E97-D   No.3   pp.406-412
Publication Date: 2014/03/01
Online ISSN: 1745-1361
DOI: 10.1587/transinf.E97.D.406
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Section on Foundations of Computer Science —New Trends in Theory of Computation and Algorithm—)
Category: Graph Algorithms
spanning distribution tree,  series-parallel graph,  flow,  supply,  demand,  partial k-tree,  

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Let G be a graph with a single source w, assigned a positive integer called the supply. Every vertex other than w is a sink, assigned a nonnegative integer called the demand. Every edge is assigned a positive integer called the capacity. Then a spanning tree T of G is called a spanning distribution tree if the capacity constraint holds when, for every sink v, an amount of flow, equal to the demand of v, is sent from w to v along the path in T between them. The spanning distribution tree problem asks whether a given graph has a spanning distribution tree or not. In the paper, we first observe that the problem is NP-complete even for series-parallel graphs, and then give a pseudo-polynomial time algorithm to solve the problem for a given series-parallel graph G. The computation time is bounded by a polynomial in n and D, where n is the number of vertices in G and D is the sum of all demands in G.